CN107942310A - The resource joint optimization method of distributed MIMO radar system multiple target location estimation - Google Patents
The resource joint optimization method of distributed MIMO radar system multiple target location estimation Download PDFInfo
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Abstract
The present invention relates to a kind of resource joint optimization method of distributed MIMO radar system multiple target location estimation, comprising：Target is specified, to minimize the maximum of multiple target position estimation error as object function；It is limited with receiving array element sum in transmitting, under conditions of transmission power gives, establish the selection of transmitting-receiving array element and distribute united resource optimization model with power；With reference to heuristic search algorithm and the convex approximate data of continuous parameter, propose to solve the mixing Boolean type combined optimization problem based on the Resource co-allocation algorithm that circulation minimizes, obtain the result of Resource co-allocation.The quantitative relation of quantified system analysis resource and ability of tracking of the present invention；Compared to element number of array, influence of the transmission power to system performance is more notable, influence of the display system resource to the precision and number of target following, more preferable system performance can be realized while system-computed amount is reduced, multiple target bulk velocity tracking accuracy is effectively improved, there is preferable actual application value.
Description
Technical Field
The invention belongs to the technical field of MIMO radar, and particularly relates to a resource joint optimization method for multi-target position estimation of a distributed MIMO radar system.
Background
The distributed MIMO radar adopts a wide-distribution antenna layout structure, has strong target detection and identification capabilities due to the characteristics of space and multiple channels, and becomes a research hotspot in the radar field. The radar resource management problem is an important component of military resource management and is also a key point for fully exerting the advantages of the MIMO radar system. Therefore, the resource optimization problem of the distributed MIMO radar is worthy of study. The joint optimization of the radar system resources is beneficial to obtaining better system performance, so that the joint optimization of the radar resources is performed from the perspective of improving the position estimation precision of the distributed MIMO radar for multi-target tracking. For the joint optimization problem of the structure and the transmission parameters of a radar system, the optimization of a receiving array element is not considered in the existing research. In fact, the number of receiving array elements has a direct influence on the system computation complexity, and meanwhile, the existing research lacks a comprehensive quantitative analysis on the overall performance of the system, so that the reference value of the research result on the practical application is very limited. Therefore, in order to reduce the processing complexity of the system and evaluate the performance of the system, the resource joint optimization problem including the selection of the receiving array elements is researched, the quantitative analysis result of the resource and the system is given, and the method has important research value.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a resource joint optimization method for multi-target position estimation of a distributed MIMO radar system, which fully schedules radar system resources and effectively improves the multi-target overall speed tracking precision.
According to the design scheme provided by the invention, the resource joint optimization method for multi-target position estimation of the distributed MIMO radar system comprises the following steps:
step 1, determining a multi-target position estimation precision function by taking a Bayesian Clarithrome boundary as a target position estimation error measurement criterion and taking the maximum value of a multi-target position estimation error as target position estimation precision;
step 2, establishing a resource joint optimization model according to the multi-target position estimation precision function;
step 3, setting the initial value K of the number of the current transmitting array element subsets 1 (ii) a According to the resource joint optimization model, adopting a heuristic greedy search algorithm to respectively select the transmitting array elements and the receiving array elements, adopting a continuous parameter convex approximation SPCA algorithm to distribute power, and carrying out iterative solution through a loop minimization algorithm to obtain an optimal resource distribution result when the maximum transmitting array element subset number is an initial value;
step 4, according to the step 3, and the value interval 1 is not more than K 1 Less than or equal to min (M, K-1), traverse K 1 And (4) value taking, namely selecting a resource allocation result with the highest positioning precision as a resource joint optimization result of the distributed MIMO radar system according to the target positioning precision, wherein M is the number of transmitting array elements in the distributed MIMO radar system.
As described above, in step 1: the Bayes Clarithrome boundary is used as a measurement criterion of the target position estimation error to obtain the Bayes Clarithrome boundary of the q target position estimation error in the k-th observation of the distributed MIMO radar systemUsing the maximum value of the multi-target position estimation error as the target position estimation precision to obtain a multi-target position estimation precision function ofWherein the content of the first and second substances,and p k Respectively representing the selected vectors of the transmit array elements tx,receiving a selection vector of an array element rx and transmitting power; and Q is the number of the moving targets.
As described above, step 2 includes the following steps: according to the total transmitting power P of the distributed MIMO radar system total And the resource joint optimization model comprises three optimization variables of transmitting array elements, receiving array elements and transmitting power is established according to the finite constraint of the total transmitting array element number K and the objective function of the target position estimation precision and the minimized target position estimation error.
In the above, the resource joint optimization model is represented as:
wherein the content of the first and second substances,p k respectively represents the transmitting array element, the receiving array element and the transmitting power of the distributed MIMO radar system during the current k-th observation,and expressing a corresponding multi-target position estimation precision function, wherein K is the size of the subset of the currently selected array elements, N is the number of the received array elements in the distributed MIMO radar system, and 1 is a full 1-column vector.
Preferably, step 3 comprises the following steps:
step 301, setting the number K of transmitting array elements in the K-th observation of the distributed MIMO radar system 1 Selection vector of transmitting array element txTransmission power p k ＝P total /K 1 1,1 is a full 1 column vector;
step 302, fix the receiving arraySelection vector of element rxAnd a transmission power p k Selecting a transmitting array element by adopting a heuristic greedy search algorithm, and solving to obtain an optimal transmitting array element;
step 303, fixing the selection vector of the transmitting array element tx according to the optimal transmitting array element obtained in step 302And a transmission power p k Selecting a receiving array element by adopting a heuristic greedy search algorithm, and solving to obtain an optimal receiving array element;
step 304, fixing the selection vector of the transmitting array element tx according to the solving results obtained in the steps 302 and 303And the selection vector of the receiving array element rxDistributing the transmitting power by adopting a continuous parameter convex approximation SPCA algorithm to obtain the current optimal transmitting power;
305, according to the current resource distribution resultp k And returning to the step 301 for iterative execution through a loop minimization method until the multi-target position estimation precision functionNo longer improved, the result of resource allocation is obtainedNamely, it isThe maximum transmitting array element subset is K 1 Time-optimized resource allocation results, corresponding transmission and receptionThe number of the array elements isThe target position estimation accuracy is
Preferably, in step 302, a vector is selected according to the received array elementAnd a transmission power p k Adopting a heuristic greedy search algorithm to select the transmitting array elements, wherein the selection comprises the following contents: selecting one array element from the unselected transmitting array elements each time to ensure that the array element is the array element with the optimal positioning precision from the unselected transmitting array elements, and simultaneously improving the estimation precision of the selected target position compared with the target position before selection; the process is circulated until the number of the selected transmitting array elements reaches K 1 OrWhen the optimization is not carried out any more, the selection of the transmitting array element is stopped; at this time, the selection result of the transmitting array element is obtained asThe number of the array elements is N tx 。
Preferably, in step 303, the product obtained in step 302 is usedTo transmit the active set, let K 2 ＝K-N tx ，Adopting a heuristic greedy search algorithm to select the receiving array elements, wherein the heuristic greedy search algorithm comprises the following contents: selecting one array element from the unselected receiving array elements each time to ensure that the array element is the array element with the optimal positioning precision from the unselected receiving array elements, and simultaneously improving the estimation precision of the selected target position compared with the target position before selection; the above-mentioned steps are repeated until the selected receiving array element is reachedThe number reaches K 2 OrStopping when no longer optimized; at this time, the selection result of the receiving array element is obtained asThe number of the array elements is N rx 。
Preferably, step 304, the result obtained according to step 302 and step 303Andthe continuous parameter convex approximation SPCA algorithm is adopted to distribute the transmitting power to obtain the current optimal transmitting power, and the method comprises the following steps: when the selection vectors of the transmitting and receiving array elements are respectivelyAndthen get the transmitted power p k Optimizing a model for optimizing a resource of a variable; allocating power of current iteration to result p' (l)，k And (5) as a linearization starting point of the (l + 1) iterations, and performing loop iteration until the result converges to a local optimal solution to obtain a power distribution result in the current state.
Further, with a transmission power p k The resource optimization model for the optimization variables is represented as:
wherein, the lambda is the signal wavelength, in order to be the power spectral density, andrespectively representDecomposed positive definite matrix and non-positive definite matrix,for parameters related to the relation between the radar and the target position,is represented by p' (l),k Is a linearized origin concave function of p' (l),k And (4) performing Taylor expansion, wherein Q is the number of the moving targets.
As described above, step 4 includes: traversing all transmitting array element subset sizes of the distributed MIMO radar system, namely according to the condition that K is more than or equal to 1 1 Less than or equal to min (M, K-1) traversal K 1 Take a value ifThen Obtaining resource federationOptimal solution for co-distribution
The invention has the beneficial effects that:
the method takes the maximum value of the minimum multi-target position estimation error as a target function, and establishes a resource optimization model combining the receiving and transmitting array element selection and the power distribution under the condition that the system transmitting power and the number of the receiving array elements allowed to be selected are limited; then, combining a heuristic search algorithm and a continuous parameter convex approximation algorithm, and solving the mixed Boolean type joint optimization problem through a resource joint allocation algorithm based on cycle minimization, wherein the heuristic algorithm is used for selecting array elements, the continuous parameter convex approximation algorithm can perform power allocation, and resource optimization allocation results are obtained through the cycle minimization algorithm; the method can improve the utilization rate of system resources and quantitatively analyze the quantitative relation between the system resources and the tracking capability while reducing the complexity of calculation and processing; compared with other algorithms, for a given radar array arrangement scene, the number of the selected array elements is constrained by the transmitting power of the system, and when the number of the selected array elements reaches a certain number, the system performance is not improved any more; the method provides important theoretical support and technical reference for the design and application of the radar system, can fully schedule the radar system resources, effectively improves the overall multi-target speed tracking accuracy, and has good practical application value.
Description of the drawings:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic flow chart of a resource joint allocation algorithm in the embodiment;
FIG. 3 is a comparison graph of the calculated amount of the algorithm in the embodiment;
FIG. 4 is a diagram of an arrangement form of radar array elements in the embodiment;
FIG. 5 is a diagram of target position estimation accuracy at different values of K in the embodiment;
FIG. 6 is a diagram illustrating the number of array elements selected according to different K values in the embodiment;
fig. 7 shows the target tracking and resource allocation results for different values of K when Q =2 in the embodiment;
FIG. 8 illustrates the ability of the system to track the number of targets in an embodiment;
fig. 9 shows the effect of the total system transmission power on the tracking performance in the embodiment, where K =10.
The specific implementation mode is as follows:
the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to improve the resource utilization rate of the distributed MIMO radar system and improve the position estimation precision of multi-target tracking, the system performance is improved through resource joint optimization. For the problem of joint optimization of the structure and the transmission parameters of a radar system, the existing research does not consider the optimization of receiving array elements, actually, the number of the receiving array elements has direct influence on the system calculation complexity, and meanwhile, the overall quantitative analysis of the overall performance of the system is lacked, so that the reference value of the research result to the practical application is very limited. To solve the problem, an embodiment of the present invention provides a resource joint optimization method for multi-target position estimation of a distributed MIMO radar system, which is shown in fig. 1 and includes the following steps:
101. determining a multi-target position estimation precision function by taking a Bayesian Clarithrome boundary as a target position estimation error measurement criterion and taking the maximum value of the multi-target position estimation errors as target position estimation precision;
102. establishing a resource joint optimization model according to the multi-target position estimation precision function;
103. setting the initial value K of the number of the current transmitting array element subsets 1 (ii) a According to the resource joint optimization model, adopting a heuristic greedy search algorithm to respectively select the transmitting array elements and the receiving array elements, adopting a continuous parameter convex approximation SPCA algorithm to distribute power, and carrying out iterative solution through a loop minimization algorithm to obtain an optimal resource distribution result when the maximum transmitting array element subset number is an initial value;
104. according to step 103, and the value interval 1 is not more than K 1 Less than or equal to min (M, K-1), traverse K 1 And (3) value taking, namely selecting a resource allocation result with the highest positioning precision as a resource joint optimization result of the distributed MIMO radar system according to the target positioning precision, wherein M is the number of transmitting array elements in the distributed MIMO radar system.
The maximum value which minimizes the error of the multi-target position estimation is taken as an objective function. Under the conditions that the total number of transmitting and receiving array elements is limited and the transmitting power is given, a resource optimization model combining transmitting and receiving array element selection and power distribution is established. Then, combining a heuristic search algorithm and a continuous parameter convex approximation algorithm, providing a resource joint allocation algorithm based on cycle minimization to solve the mixed Boolean type joint optimization problem; the system can realize better system performance while reducing the system calculation amount.
In a second embodiment, referring to fig. 2, a resource joint allocation method for multi-target position estimation in a distributed MIMO radar system specifically includes the following steps:
step 1: and deducing a target position estimation precision expression, and taking the maximum value of the multi-target position estimation errors as the overall position estimation precision of the system.
The distributed MIMO radar system is assumed to contain M transmitting radars and N receiving radars, each radar is a single-antenna radar, and each partThe radar spacing is sufficiently large. In a two-dimensional plane, the coordinates of the transmitting radar areReceive radar coordinates ofThe radar emits orthogonal signals, the low pass is equivalent to s m (t), m =1,L,M, satisfyingT m The mth radar transmission signal duration. The transmitting power vector of the radar is p k ＝[p 1,k ,p 2,k ,L,p M,k ] T ，p m,k ＝E m f r ，E m Energy of a single pulse, f r For pulse repetition frequency, the signal bandwidth vector is beta k ＝[β 1,k ,β 2,k ,L,β M,k ] T The signal duration vector is t k ＝[t 1,k ,t 2,k ,L,t M,k ] T 。
Suppose there are Q moving objects in the scene, and the position state of the object is (x) q ,y q ) Q =1,L, Q, speed state ofAt the k-th observation, the state vector of the target q isIts motion model can be expressed as
Wherein F is the state transition matrix of the target,representing a zero mean, white Gaussian process noise sequence with a covariance matrix of Q k . When the target moves at a constant speed, the target moves,
where Δ t denotes the sampling time interval, q 0 Representing the intensity of process noise, I 2 A 2 x 2 unit array is represented,is the sign of the kronecker product.
For the convenience of research, it is assumed that each receiving end of the distributed MIMO radar system can implement time synchronization. At the k-th observation of the target, the low-pass equivalent signal received by the nth part receiving radar can be expressed as
Mqn represents the whole path of the signal emitted from the m-th part transmitting radar, reflected by the q-th target and received by the n-th part radar; a is mqn,k Represents a path loss factor, is related to the target-to-radar distance and the signal carrier frequency,f c is the carrier frequency, and is,andthe Euclidean distances from the target to the transmitting and receiving radar, respectively, are defined as
ζ mqn,k A complex scattering coefficient representing a radar cross-sectional area of the target; t is t mqn Represents signal time delay and satisfiesc is the speed of light; omega mqn,k Indicating the Doppler frequency shift generated by the movement of the target
Lambda is the wavelength of the signal and,andthe observation angles of the m-th transmitting radar and the n-th receiving radar to the target q are respectively set; w is a n,k (t) represents an autocorrelation function ofThe white gaussian noise of (1) is,is the power spectral density.
At each moment, the fusion center tracks the target according to the time delay and Doppler information of the received data, and the nonlinear observation process can be described as
Wherein f (-) represents the observation process,is observed white gaussian noise.
Cramer-Rao bound and of parameter estimation at high signal-to-noise ratioThe unbiased estimates are very close. For a moving target, bayesian clalmelo bounds may be employed as a metric criterion for target parameter estimation. The Clarithrome matrix defining the state estimate for the qth target isState vector of targetContains 4 state components and, therefore,is a 4 x 4 matrix whose diagonal elements are the lower bounds of the variance of the respective state estimation components, wherein the position estimation error of the target satisfiesFor the resource optimization problem of array element selection and power allocation combination, the position estimation precision function of the qth target can be approximately expressed as
Wherein the content of the first and second substances,a vector is selected for the transmitting array element,a vector is selected for the received array elements,0 means discard and 1 means pick. In relation to radar and target positionThe parameters are respectively defined as
Wherein the content of the first and second substances,
in order to better master the overall tracking accuracy of multiple targets, the target position estimation accuracy with the maximum value of the multiple target position estimation errors as a whole is defined. Thus, the multi-target position estimation accuracy function herein is
Step 2: under the constraint of system resources, a multi-resource joint optimization model is established by taking the minimum target position estimation error as an objective function, and array elements are transmittedReceiving array elementTransmission power p k The resource joint optimization model of the three optimization variables is as follows:
k is the size of the selected array element subset; p total Is the total transmit power of the system;respectively as the optimal distribution result of transmitting array element, receiving array element and transmitting power.
And step 3: setting an initial value K of the number of transmitting array elements 1 ，p k ＝P total /K 1 ·1。
And 4, step 4: fixed receiving array elementAnd a transmission power p k And solving the optimal transmitting array element.
According toAnd p k And (4) adopting a heuristic greedy search algorithm to select the transmitting array elements. One array element is selected from the unselected transmitting array elements each time, so that the array element is the array element with the optimal positioning precision in the unselected transmitting array elements, and meanwhile, the estimation precision of the selected target position is improved compared with that before selection. The operation is repeated until the number of the selected transmitting array elements reaches K 1 OrAnd when the optimization is not carried out any more, the selection of the transmitting array element is stopped. At this time, the selection result of the transmitting array element is obtained asThe number of the array elements is N tx 。
And 5: fixed transmitting array elementAnd a transmission power p k And solving the optimal receiving array element.
To be provided withTo transmit the active set, let K 2 ＝K-N tx ，And selecting the receiving array elements by adopting a heuristic greedy search algorithm. And selecting one array element from the unselected receiving array elements each time to ensure that the array element is the array element with the optimal positioning precision from the unselected receiving array elements, and simultaneously improving the estimation precision of the selected target position compared with the target position before selection. The operation is circulated until the number of the selected receiving array elements reaches K 2 OrStopping when no longer optimized. At this time, the selection result of the receiving array element is obtained asThe number of the array elements is N rx 。
And 6: fixed transmitting array elementAnd receiving array element variablesAllocating optimal transmit power
According to the selected array element subsetAndthe transmission power is distributed by adopting an SPCA algorithm to obtain a transmission power distribution result p k And the position estimation accuracy of the targetThe SPCA algorithm has the main idea that a non-convex function is decomposed into the sum of a convex function and a concave function, and then the Taylor expansion of the concave function near a certain point is approximated to a linear function to solve by utilizing the linear characteristic of the concave function near the certain point. The following describes the power allocation using the SPCA algorithmAnd (4) processing.
When the selection vectors of the transmitting and receiving array elements are respectivelyAndat a transmission power p k The resource optimization model for optimizing variables can be expressed as
Order to The optimization model of the above formula can be expressed as
According to the SPCA algorithm, the first non-linear constraint can be decomposed into a sum of a convex function and a concave function. Will now beDecomposition into positive definite matricesAnd a non-positive definite matrixWhen, the above formula can be expressed as
Wherein, in the step (A),p′ k in the form of a convex function, the function,p′ k is a concave function. Is of p' (l),k For linearization starting point, the concave function is at p' (l),k Is processed intoThereby the above formula is converted into
Allocating power of current iteration to result p' (l),k And (5) as a linearization starting point of the (l + 1) iterations, and performing loop iteration until the result converges to a local optimal solution to obtain a power distribution result in the current state.
And 7: and obtaining the optimal resource allocation result under the current transmitting subset size.
By means of a cycle minimization. For the current K 1 And further optimizing the value-taking resource allocation result. According to the current informationSource allocation resultp k Repeating the steps 3-6 until the resource allocation resultIs not further improved, and the resource allocation result is obtained asAt this time, the process of the present invention,the maximum transmitting array element subset is K 1 The optimal resource allocation result is that the corresponding transmitting and receiving array elements have the numberThe target position estimation accuracy is
And 8: and traversing all the sizes of the transmitting subsets to obtain the optimal resource allocation result of the system at the current moment.
Traverse K 1 The value of (a). If it isThen Thereby obtaining the optimal solution of the resource joint allocation
In the invention, a target is specified, and the maximum value of the minimum multi-target position estimation error is taken as a target function; under the conditions that the total number of transmitting and receiving array elements is limited and the transmitting power is given, a resource optimization model combining transmitting and receiving array element selection and power distribution is established; and (3) combining a heuristic search algorithm and a continuous parameter convex approximation algorithm, and solving the mixed Boolean joint optimization problem by a resource joint allocation algorithm based on cycle minimization to obtain a resource joint allocation result. The invention quantitatively analyzes the quantitative relation between system resources and tracking ability; for a given radar array arrangement scene, the system performance is not improved when the number of the selected array elements reaches a certain number under the constraint of the system transmitting power, wherein the number of the transmitting array elements required by the system is obviously less than that of the receiving array elements; compared with the number of array elements, the influence of the transmitting power on the system performance is more obvious.
Based on the above embodiments, to further verify the effectiveness of the present invention, the following further explains the present invention by using the specific example of the third embodiment:
1) Algorithmic computation analysis
Specific algorithm referring to fig. 2, the selected size of the transmit array element subset is K 1 The number of times of selecting the generated transmitting array element isThe number of times of selecting the receiving array element isSubsequently, 1 power optimization operation is generated. When the number of the minimum cycle times is gamma and the size of the array element subset is K, the total number of the array element selection times isThe power distribution times are gamma (min (K-1,M) -max (K-N, 1) + 1). If the exhaustive array element combination mode is adopted, power optimization needs to be carried out for 1 time on each group of array element combination, and the generated array element selection and power optimization times are bothWhen the selected array element subsets K are different, the number of array element selection and power optimization generated by the two is shown in fig. 3, where: (a) Is an arrayThe element selection times are shown schematically, and (b) is a power optimization times diagram. Assuming that the loop minimization iteration number γ =5 (average of actual operation statistics), M = N =10. It can be seen that the proposed algorithm has the advantage of reducing the computational load in both array element selection and power allocation when the system does not select all array elements.
2) Simulation conditions are as follows:
in order to verify the effectiveness of the algorithm, the working capacity of the radar system is further evaluated, and a simulation experiment is carried out. In an experimental scenario of 20km × 20km, an array position of a distributed MIMO radar system with M = N =10 is fixed, as shown in fig. 4. Total transmitting power P of radar system total =10kw, the system bandwidth of the individual radar is β =5MHz, and the radar carrier frequency is f c =1GHz and pulse repetition frequency f r =5kHz. To simplify the model, assume a target scattering coefficient | ζ | =1. Q targets exist in a scene, the Q targets all perform uniform linear motion at the speed of 100m/s, the target observation time interval is T =5s, and the tracking times are 10 times. The number of transmitting and receiving array elements allowed by the system is K. In order to better analyze the number Q of the targets, the number K of the array elements and the influence of the number relation between the transmitting array elements and the receiving array elements on the target tracking capability, the performance of the system is evaluated respectively from two aspects of target motion track determination and random distribution. The monte carlo number used for the experiment was 500.
3) Simulation experiment:
assuming that the number of targets is Q =2, the motion trajectory thereof is shown in fig. 4. Now, resource joint allocation is performed on three different array element subset value conditions of K =6,12,18, and the obtained target position estimation accuracy is shown in fig. 5, and the corresponding array element selection result is shown in fig. 6, where: the schematic diagram of (a) showing the total number of the selected array elements, (b) showing the number of the selected transmitting array elements, and (c) showing the number of the selected receiving array elements. As can be seen from fig. 5, the larger the array element subset size K is, the higher the position estimation accuracy of the target is, and compared with the improvement amount of the performance when K is increased from 6 to 12, the performance improvement effect is weaker when K is increased from 12 to 18, thereby illustrating that there is not a linear relationship between the system performance and the selected number of array elements. As can be seen from fig. 6 (a), the number of actual array elements may be smaller than the maximum number of array elements allowed by the system. In fact, for a radar system with limited system total power, when the number of array elements is increased to a certain degree, the system performance is not improved any more due to the limitation of the transmission power. In addition, as shown in fig. 6 (b) and fig. 6 (c), the number of transmitting elements selected by the system is less than the number of receiving elements.
To better analyze the performance of the proposed algorithm, the target motion trajectory is now simulated randomly in the radar constellation form of fig. 4. According to the position estimation precision of the system to the target, defining the target tracking precision mu to represent the maximum value of the position estimation error in the target tracking process of the system, namely when the total power P of the system is P total The array element subset size K and the number of targets Q are given, and the position estimation error of any target in the experimental scene at any time does not exceed μ. Under this condition, fig. 7 shows the target tracking and resource allocation results under different K values when Q =2, where in fig. 7: (a) The schematic diagram shows the tracking precision of the system to the target, and (b) the schematic diagram shows the quantity relation of the selected array elements. From the tracking precision result of the system in fig. 7 (a) on the target, it can be seen that the larger the array element subset size K is, the smaller the error of the system on the target tracking is, and the stronger the tracking capability is. For each goal of Q =2, when K is&And when the voltage is more than 10, the tracking capability of the system gradually tends to be stable. Fig. 7 (b) shows the corresponding array element selection quantity relationship. It can be seen that when K is more than or equal to 10, the number of the actually selected array elements is in proportion to the allowable subset of the systemThe fast decrease is started, although the size K of the selectable array element subset is increased, the number of the actually selected array elements is increasedAnd is not increased. Ratio of transmitting and receiving array elements to selected array elementsAnd also tends to be stable. It can be seen that when the array element allows the subset size K to be more than or equal to 10, the system tracking capability basically reachesAnd when the optimal value is reached under the condition, the number of the selected transmitting array elements is about 1/3 of the number of the selected receiving array elements. The results are consistent with FIG. 7 (a).
The tracking ability of the radar system can be evaluated not only from the position estimation accuracy of the system on the target, but also from the number of tracked targets. Considering practical conditions, the system may also put specific requirements on the tracking accuracy μ of the target. Fig. 8 shows a relationship diagram between different K values and tracking accuracy requirements μ and the number Q of targets tracked by the system, where in fig. 8: (a) A schematic diagram showing the number of tracked targets under different K values when the tracking accuracy μ =10m, and (b) a schematic diagram showing the number of tracked targets with different tracking accuracy requirements μ when K =10. It can be seen that the number of the system tracking targets is gradually increased along with the increase of the size K of the array element subset and the target tracking precision mu. As can be seen from fig. 8 (a), when the tracking accuracy requirement is μ =10m, the number of targets tracked by the system is very limited by increasing the array element subset size K. Because the total power resource of the system is limited, the size K of the array element subset is increased, and the continuous improvement of the tracking capability cannot be brought. When the size of the array element subset is K =10 in fig. 8 (b), the larger the target tracking accuracy μ is, that is, the lower the tracking accuracy requirement is, the faster the number of targets tracked by the system increases.
In order to better analyze the influence of system power resources on system performance, fig. 9 analyzes the influence of different powers on the accuracy and the number of targets tracked by the system, where in fig. 9: (a) A schematic diagram showing target accuracy corresponding to different transmission powers when the target number Q =3, and (b) a schematic diagram showing the number of tracking targets corresponding to different transmission powers when the system tracking accuracy μ =10 m. It can be seen that the higher the transmission power is, the higher the tracking accuracy of the target is, and the more the tracking number is. As can be seen from fig. 7 (a) and fig. 9 (a), increasing system resources can improve the tracking accuracy of the target within a certain limit, but as the system resources increase, the performance is improved more and more slowly. As can be seen from fig. 8 (b) and 9 (b), the number of tracking targets can be greatly increased by properly relaxing the tracking accuracy requirement or increasing the transmission power.
Through analysis, for a given radar array arrangement scene, the system performance is not improved any more when the number of selected array elements reaches a certain degree under the constraint of the system transmitting power. Selecting too many array elements brings more data processing complexity. In addition, the number of transmitting array elements selected by the system is obviously less than that of receiving array elements. This has reference significance to the actual radar system design. The simulation analysis shows that the influence of different array element subsets and the influence of the transmitting power on the accuracy and the number of the system tracking targets are more obvious than the influence of the system array elements on the system performance, and the influence of the increase of the resources on the improvement of the number of the tracking targets is more prominent than the improvement of the tracking accuracy. Experiments further investigated the quantitative relationship between target accuracy and number. Providing data support for practical application of the system.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A resource joint optimization method for multi-target position estimation of a distributed MIMO radar system is characterized by comprising the following steps:
step 1, determining a multi-target position estimation precision function by taking a Bayesian Clarithrome boundary as a target position estimation error measurement criterion and taking the maximum value of a multi-target position estimation error as target position estimation precision;
step 2, establishing a resource joint optimization model according to the multi-target position estimation precision function;
step 3, setting the initial value K of the number of the current transmitting array element subsets 1 (ii) a According to the resource joint optimization model, adopting a heuristic greedy search algorithm to respectively select the transmitting array elements and the receiving array elements, and adopting continuous parameter convex approximation SPThe CA algorithm carries out power distribution and iterative solution is carried out through a loop minimization algorithm to obtain an optimal resource distribution result when the number of the maximum transmitting array element subsets is an initial value;
step 4, according to the step 3, and the value interval 1 is not more than K 1 Less than or equal to min (M, K-1), traverse K 1 And (4) value taking, namely selecting a resource allocation result with the highest positioning precision as a resource joint optimization result of the distributed MIMO radar system according to the target positioning precision, wherein M is the number of transmitting array elements in the distributed MIMO radar system.
2. The method for resource joint optimization for multi-objective position estimation of a distributed MIMO radar system as claimed in claim 1, wherein in step 1: the Bayes Clarithrome boundary is used as a measurement criterion of the target position estimation error to obtain the Bayes Clarithrome boundary of the q target position estimation error in the k-th observation of the distributed MIMO radar systemUsing the maximum value of the multi-target position estimation error as the target position estimation precision to obtain a multi-target position estimation precision function ofWherein the content of the first and second substances,and p k Respectively representing the selection vector of the transmitting array element tx, the selection vector of the receiving array element rx and the transmitting power; and Q is the number of the moving targets.
3. The method for resource joint optimization for multi-objective position estimation of distributed MIMO radar system according to claim 2, wherein step 2 comprises the following steps: according to the total transmitting power P of the distributed MIMO radar system total And the finite constraint of the total transmitting array element number K, establishing a transmitting array element and a receiving array element according to a multi-target position estimation precision function and taking the minimum target position estimation error as a target functionAnd a resource joint optimization model of three optimization variables of the transmitting power.
4. The method for resource joint optimization for multi-objective position estimation of the distributed MIMO radar system as claimed in claim 3, wherein the resource joint optimization model is expressed as:
wherein the content of the first and second substances,p k respectively represents the transmitting array element, the receiving array element and the transmitting power of the distributed MIMO radar system during the current k-th observation,and expressing a corresponding multi-target position estimation precision function, wherein K is the size of the currently selected array element subset, N is the number of the received array elements in the distributed MIMO radar system, and 1 is a full 1-column vector.
5. The method for resource joint optimization for multi-objective position estimation of distributed MIMO radar system as claimed in any one of claims 1 to 4, wherein step 3 comprises the following steps:
step 301, setting the number K of transmitting array elements in the K-th observation of the distributed MIMO radar system 1 Selection vector of transmitting array element txTransmission power p k ＝P total /K 1 1,1 is a full 1 column vector;
step 302, fix rx selection vector of receiving array elementAnd a transmission power p k Selecting a transmitting array element by adopting a heuristic greedy search algorithm, and solving to obtain an optimal transmitting array element;
step 303, fixing the selection vector of the transmitting array element tx according to the optimal transmitting array element obtained in step 302And a transmission power p k Selecting a receiving array element by adopting a heuristic greedy search algorithm, and solving to obtain an optimal receiving array element;
step 304, fixing the selection vector of the transmitting array element tx according to the solving results obtained in the steps 302 and 303And selection vector of receiving array element rxDistributing the transmitting power by adopting a continuous parameter convex approximation SPCA algorithm to obtain the current optimal transmitting power;
305, according to the current resource distribution resultp k And returning to the step 301 for iterative execution through a loop minimization method until the multi-target position estimation precision functionNo longer improved, the resource allocation result is obtained asNamely, it isThe maximum transmitting array element subset is K 1 The optimal resource allocation result is that the corresponding transmitting and receiving array elements have the numberThe target position estimation accuracy is
6. The method for joint resource optimization for multi-objective position estimation in distributed MIMO radar system as claimed in claim 5, wherein in step 302, the vector is selected according to the received array elementsAnd a transmission power p k Adopting a heuristic greedy search algorithm to select the transmitting array elements, wherein the selection comprises the following contents: selecting one array element from the unselected transmitting array elements each time to ensure that the array element is the array element with the optimal positioning precision from the unselected transmitting array elements, and simultaneously improving the estimation precision of the selected target position compared with the target position before selection; the operation is repeated until the number of the selected transmitting array elements reaches K 1 OrWhen the optimization is not carried out any more, the selection of the transmitting array element is stopped; at this time, the selection result of the transmitting array element is obtained asThe number of the array elements is N tx 。
7. The method for joint resource optimization for multi-objective position estimation in distributed MIMO radar system as claimed in claim 5, wherein in step 303, the values obtained in step 302 are usedTo transmit the active set, let K 2 ＝K-N tx ，Adopting a heuristic greedy search algorithm to select the receiving array elements, wherein the heuristic greedy search algorithm comprises the following contents: selecting one array element from the unselected receiving array elements each time to ensure that the array element is the array element with the optimal positioning precision from the unselected receiving array elements, and simultaneously improving the estimation precision of the selected target position compared with the target position before selection; the operation is circulated until the number of the selected receiving array elements reaches K 2 OrStopping when no longer optimized; at this time, the selection result of the receiving array element is obtained asThe number of the array elements is N rx 。
8. The method for joint resource optimization for multi-objective position estimation in distributed MIMO radar system as claimed in claim 5, wherein in step 304, the values obtained from step 302 and step 303 are usedAndthe continuous parameter convex approximation SPCA algorithm is adopted to distribute the transmitting power to obtain the current optimal transmitting power, and the method comprises the following steps: when the selection vectors of the transmitting and receiving array elements are respectivelyAndthen get the transmitted power p k Optimizing a model for optimizing a resource of a variable; allocating power of current iteration to result p' (l),k As l +1And (5) circularly iterating the linearization starting point of the secondary iteration until the result is converged to a local optimal solution, and obtaining a power distribution result in the current state.
9. The method of claim 8, wherein the joint optimization of resources for multi-objective position estimation in distributed MIMO radar system is performed at a transmission power p k The resource optimization model for the optimization variables is represented as:
wherein, the lambda is the signal wavelength, in order to be the power spectral density, andrespectively representDecomposed positive definite matrix and non-positive definite matrix,for parameters related to the radar and target position relationship,is represented by p' (l),k Is a linearized origin-concave function of p' (l),k And (4) performing Taylor expansion, wherein Q is the number of the moving targets.
10. The method for joint resource optimization for multi-objective position estimation in a distributed MIMO radar system as claimed in claim 4, wherein step 4 comprises: traversing all transmitting array element subset sizes of the distributed MIMO radar system, namely according to the condition that K is more than or equal to 1 1 Less than or equal to min (M, K-1) traversal K 1 Take a value ifThen the Obtaining an optimal solution for joint allocation of resources
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